Transformative semalgebraic ontology posits transformation as “the primary ontological primitive: to be is to be transformable, and what we call entities are stable regions within fields of admissible variation”[1]. Bonisoli begins constructing a semantic algebra to understand the nature of transformations, looking toward a general apparatus that incorporates numerical-quantitative frameworks into a semanticisation of ontological transformations. Enframing this apparatus in a set of nested convergences, invoking Euclidean geometry as a fold of Riemannian space, there is an attempt to move beyond metaphor into a fully semantic-algebraic topology of relations and conditions.
OTS is a formalisation of disparate ontological threads, encompassing topology, algebraic geometry, linguistics, uncertainty and virtuality. From this vortex Bonisoli conceptualises the essences of transformation in physicalist and mathematical operations. At its heart are the concepts of potentia and the virtual as the forces between becoming and being, the indecisive tension of being’s lack and the omnipresent shadow of the other (the un-, the anti-) above the ontic.
“A structure can be read as a stable configuration of admissible transformations; a relation, as the trace of a transformation that can be performed between two semantic regions; an inferential role, as the network of transformations that a semantic entity can sustain without ceasing to be itself; an interaction, in the physical sense, as a transformation of state so successfully constrained — by physical law, by experimental conditions, by geometry — that it reads as fact rather than as possibility”[2].
Relationality as a transformational boundary beyond the ontic but also encompassing the facticity of the ontic as a settled state of bounded reality. Reality is a constraint upon the potential of transformation, centring settled being (the they-self[3]) and its associated tools and devices as the paradigmatic node in this network topology. OTS’s two central axioms further develop this tension. “Thinking as transforming” and “structural ontological unknowability” present both the potential of an expanding other (as an interstitial or liminal potential between virtuality and actuality) and the physical limits of thinking itself (in its inability to be totalising).
So far, we are well within the philosophical corpus recognising the potentiality of thought and the structural limits of knowledge. Spinoza’s relations of substances or Nietzsche’s will to power frame similar tensions of possibility and actualisation in ontical situations. The formalisation of transformation through semantic atoms (the elemental unit of admissible dispositions), non-idempotency, thought-structured operators (intelligence, non-causal initiators and mitotic operators), and actualised and unactualised tensor fields demonstrates a structure of potentiality within a semalgebraic geometry.
Its applications are wide-ranging, from LLM syntax and the model-theoretic limits of quantum mechanics and M-theory to epistemology and the production of political ideologies. However, there appear to be innate limitations to its understandings of ontology due to occlusions fundamental to the explanatory model.
“Its specific contribution is to propose that transformation can be treated as the primitive common to these displacements, and that this primitive can be formalized semantically. The Semalgebra does not claim to be the final language of process, structure, inference, manifestation, or emptiness. It claims to provide an apparatus in which transformation can be operationally distinguished from repetition, recombination, stabilization, deformation, and collapse”[4]. In centring transformation as an ontological explanandum, other forms of relationality or thinking are treated as secondary explanans of it. Going beyond operational distinction, it attempts to ground transformation as the ur-variable from which being and its limitations emerge.
The section on pedagogy reveals this acutely, delineating the limits of thought – “a transformation that violates the boundary conditions of the field becomes distortion, not insight. A metaphor that cannot maintain admissible compositional signatures becomes category error. A creative answer that abandons the constraints of the problem is not pseudo-hyperbolic novelty but failed geodesic passage. The value of the apparatus lies precisely in distinguishing transformation from mere deviation”[5]. But the forms of admissibility are never grounded beyond a perfunctory framework of tension between becoming and being. To think is to be able to fall into creative lacunae, whether productive or unproductive. Prioritising the former mirrors a productivist framing amenable to the demands of capital.
Fundamental ontology as transformation becomes ungrounded as a value structure emerges that limits the lines of flight from virtual to actual. The ontic takes over as a framing of being-in-the-world which thereby limits what can be thought and what is classed as a deviation. We end up in a circle of constant revaluation without exploring the nature of valuation itself. It is assumed that actualisation and insight are contiguous. A framework for innovation in a capitalist realist[6] sense invades and restricts virtual potential, turning neither to the real nor the other beyond but to the actual-ontic as the pathway of thought. SATOM combinatorics within tensor fields cannot envisage collapse, repetition or destruktion as anything more than deviations from an admissible norm. OTS is the ontologisation of progressive teleology, the delimitation of actualisability.
Of course, at the level of the banal, physical limits will delimit the nature of the actual across spacetime. However, to confuse physicalist or tropistic forces with creative willing is to maintain a humanistic centrality that both assumes we are factically bounded and that within this boundary we have free rein. Bonisoli’s addition of free will via non-causal initiation fulfils the function of this centralisation, allowing for non-idempotent thought within a curved geometric field. It is a Cartesian refuge that limits thinking and opens spacetime, jerry-rigging one model-theoretic structure onto another.
Thought can escape this binding frame, as Bonisoli states when distinguishing transformation from other ontological forms. Thought is not limited by a Cartesian ontology of the centred I or the attenuations of a free will. To think being is to think around the void, to both face and escape the real, to move beyond the limits of the I-self and they-self that cannot face being. Transformation as a fundamental becomes another deflection of fundamental ontology, making being a telos of innovation or productive thought. The valuation of productivity remains unquestioned, buried beneath epistemological assumptions and mathematical axioms.
Bonisoli’s work around black hole event horizons and political ideology reveal the unspoken valuative aspects of this ontology. On the former, the limits of transformation’s admissibility are revealed in the inability to grasp the limits of the actual itself. It is reframed from the inactualisable to the limits of transformability that appears again to fall into the banality of physicalist limits. “What distinguishes the black-hole case is the kind of absence at issue. In OTS, the relevant absence is not the absence of being but the absence of outward transformability. The black hole is therefore a boundary-structured interruption in the network of transformability. It is not a thing first and a boundary second; it is a boundary-defined failure of outward actualisation”[7]. This is a distinction without a difference in a framework that positions transformation as the key aspect of being. The event horizon represents both the limits of the real and the limits of perception. The former in that there is nothing known beyond it except for theoretical excreta in the form of Hawking radiation. The latter in that temporality itself breaks down. The temporal relation between outside and inside observers ends. This is ontological collapse as being is entirely encompassed by the void of the real (the end of the real as a universal field). Both real and actualisable are framed by sapient perception. Being as the they is re-encoded onto an event horizon that ensures the removal of the they as the inside observer would be relegated to a purely private perceptual locus. The ability to describe, to establish a frame of reference, is destroyed.
Inactualisation entails the collapse of being in the outer limits of the real. Beyond speculative imaginings of transformations beyond a black hole, going toward a theological physics of white holes and transferable matter (something which OTS would deem a deviation from creative potential), being’s limit is in the event horizon, moving away from a framework of transformation toward breakdown. Conceiving relational islands attempts to maintain a human grasp on such ontological limits, retreating from being-towards-death and back into the relational field of they-selves. A reclamation of the admissible as a value structure to interpret the real.
Bonisoli’s analysis of political ideology and transreality furthers the essence of OTS as an ontologisation of present value structures. Transreality is “the creeping replacement of objective reality with a seamless blend of misinformation, speculation, and disinformation”[8]. The underlying assumption being that an informational clarity premised on truth pre-existed the internet or social media. This is a valuative blindness reliant on liberal modernity being a paragon of objectivity (assuming the nature of said objectivity from the start).
Bonisoli’s solution to this internet-induced informational fugue is laughable. “Resistance of a revolting people: a conscious, organized refusal to be ruled by invisible powers – whether mythic, technological, or institutional. Like a society that rises up against its would-be masters, the ‘swarm’ of citizens, equipped with radical transparency and genuine agency, transforms from a passive object of manipulation into an active, creative subject of governance”[9]. How is such agency to be equipped? An act of God? Maybe via the return of a “primeval will” that supposedly inhabited the internet’s founders (many of whom created systems reliant on constant engagement by their users). The fundamental question of why humanity went from a state of informational clarity to dark mythopoesis is never asked, precisely because asking it undergirds the shallowness of the ontological reductions required to arrive at the conclusion of transreality.
OTS as a framework posits innovative adaptivity as the means of being-in-the-world. Informational fugue or the limits of being bring into question the forms of such adaptivity and how limited it really is in a world of competing wills and non-sapient forces. OTS, as a kind of capitalist ontology (the interiorisation of exterior controls and barriers into a dialectic), centres human agency as the field of tension between becoming and being. Deviations from this field are non-ontological (or of a being that cannot be conceived), but the fundaments of ontology are dodged by the reversion to an unacknowledged value structure whereby transformation is being and being is transformation. Rather than a field of tension, what Bonisoli has constructed is a field of admissibility whose limits are inscribed the moment thought drifts to the inhuman, a-human or non-I/non-they. The void, where it is conceived, is little more than the limit of transformation itself, continuing the tautological avoidance of being as looking-into-the-void. Thought is prescribed, already limited to SATOM pathways that can continue a post-valuative productive creativity.
A semalgebraic geometrisation of ontological transformation is a fascinating project for formalising lines of flight between virtual and actual planes, mapping various beings (being-as-transformation; being-as-repetition; being-into-collapse; destruktion, etc.) and their potential pathways through conceptual space. But as with any map, this a rationalisation of pre-existing relations with valuative structure added on. Far from fundamental ontology, Bonisoli is ontologising values of the present, presenting presence as the encompassing of being. Better to begin picking at the nature of its unknowability (something Bonisoli acknowledged in his second axiom) and placing this framework in relations of being and non-being. Let it fall into the void rather than become another hubristic project of sapient centrality that forecloses historical overturning.
[1] https://philarchive.org/rec/BONTAO-16
[2] https://philarchive.org/rec/BONTAO-16
[3] Martin Heidegger – Being and Time
[4] https://philarchive.org/rec/BONTAO-16
[5] https://philarchive.org/rec/BONTAO-16
[6] Mark Fisher – Capitalist Realism: Is There No Alternative?
[7] https://philarchive.org/rec/BONBHI
[8] https://www.futuri-journal.org/index.php/futuri/article/view/241
[9] https://www.futuri-journal.org/index.php/futuri/article/view/241